Question

Solve the equation by factoring. 3x^2-5x-12=0

Answer 1

x = 3

`x=-1(1)/(3)` or
`x=-(4)/(3)`

Explanation:

3x² - 5x - 12 = 0

Method 1: Factoring

3x² + 4x - 9x - 12 = 0

(3x² + 4x) + (- 9x - 12) = 0

x(3x + 4) - 3(3x + 4) = 0

(x - 3)(3x + 4) = 0

Two separate equations

x - 3 = 0

3x + 4 = 0

x - 3 = 0

x - 3 + 3 = 0 + 3

3x + 4 = 0

3x + 4 - 4 = 0 - 4

3x = - 4

`(3x)/(3) :-(4)/(3)`

`x=-1(1)/(3)`

Method 2: Quadratic Formula

Ignore the A before the ±, it wouldn't let me type it correctly.

`x=\frac{-b±\sqrt{b^(2) -4ac} }{2a}`

3x² - 5x - 12 = 0

a = 3

b = - 5

c = - 12

`x=\frac{-(-5)±\sqrt{(-5)^(2) -4((3)(-12))} }{2(3)}`

`x=(-(-5)±√(25 -4((3)(-12))) )/(2(3))`

`x=(-(-5)±√(25 +144) )/(2(3))`

`x=(-(-5)±√(169) )/(2(3))`

`x=(-(-5)±13)/(2(3))`

`x=(5±13)/(6)`

Two separate equations

One must have a + (positive) and the other will have a - (negative).

`x=(5+13)/(6)`

`x=(18)/(6)`

x = 18 ÷ 6

x = 3

`x=(5-13)/(6)`

`x=(-8)/(6)`

x = - 8 ÷ 6

`x=-1(1)/(3)`

Answer 2

hope this helps you out! :)